How to start and stop movie sequence of image node at specific frame in python script?
Not sure how to answer but I am trying to access the start_frame parameter of a sequence strip in the VSE and my guess is it has to do with this thing called context. Looks like where ever the start_frame is being defined or allocated in it's parameter the context is where it is inherited.
So it seems you have to create a context which is local to your script so any called functions to "play at some start_frame" will be assigning the "start_frame" from a locally created/allocated "context". 
See:
https://blenderartists.org/t/solved-add-effect-strip-transform-for-image-vse-lm18/688456/2
and Ctrl+F: You just need to set the context.

I have read however, this is not so good for when the local allocation is un-allocated you then have a reference which points to ??? or is broken and a potential for blender crash.
See: 
https://docs.blender.org/api/current/info_gotcha.html
and Ctrl+F: # polygons have been re-allocated

Sounds like there is a start_frame being set from a GLOBAL context in your case so every start_frame=1 and that is a context you have to modify. Good luck I'm just trying to get:
bpy.ops.sequencer.effect_strip_add(frame_start=frame_start, frame_end=frame_end, type=‘SPEED’)
to use a frame_start from the selected strip and I don't know how to pass a frame_start parameter which equals the frame_start of the already selected strip without having to recreate a new context. I would imagine I could pass by reference but where is the allocated reference? 

Anyway the answer is in the inherited context it seems.